High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

Abstract

A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.

Substantial changes including the title and the content of the paper 8 pages, 2 figures, 3 tables

References in corpus (2)

• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• Symmetric Triple Well with Non-Equivalent Vacua: Instantonic Approach

Cited by in corpus (3)

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• Eigenvalues from power--series expansions: an alternative approach